伍德里奇计量经济学英文版各章总结.docx

伍德里奇计量经济学英文版各章总结.docx

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伍德里奇计量经济学英文版各章总结

CHAPTER1

TEACHINGNOTES

YouhavesubstantiallatitudeaboutwhattoemphasizeinChapter1.Ifinditusefultotalkabouttheeconomicsofcrimeexample（Example1.1）andthewageexample（Example1.2）sothatstudentssee,attheoutset,thateconometricsislinkedtoeconomicreasoning,eveniftheeconomicsisnotcomplicatedtheory.

Iliketofamiliarizestudentswiththeimportantdatastructuresthatempiricaleconomistsuse,focusingprimarilyoncross-sectionalandtimeseriesdatasets,asthesearewhatIcoverinafirst-semestercourse.Itisprobablyagoodideatomentionthegrowingimportanceofdatasetsthathavebothacross-sectionalandtimedimension.

Ispendalmostanentirelecturetalkingabouttheproblemsinherentindrawingcausalinferencesinthesocialsciences.Idothismostlythroughtheagriculturalyield,returntoeducation,andcrimeexamples.Theseexamplesalsocontrastexperimentalandnonexperimental（observational）data.Studentsstudyingbusinessandfinancetendtofindthetermstructureofinterestratesexamplemorerelevant,althoughtheissuethereistestingtheimplicationofasimpletheory,asopposedtoinferringcausality.Ihavefoundthatspendingtimetalkingabouttheseexamples,inplaceofaformalreviewofprobabilityandstatistics,ismoresuccessful（andmoreenjoyableforthestudentsandme）.

CHAPTER2

TEACHINGNOTES

ThisisthechapterwhereIexpectstudentstofollowmost,ifnotall,ofthealgebraicderivations.InclassIliketoderiveatleasttheunbiasednessoftheOLSslopecoefficient,andusuallyIderivethevariance.Ataminimum,Italkaboutthefactorsaffectingthevariance.Tosimplifythenotation,afterIemphasizetheassumptionsinthepopulationmodel,andassumerandomsampling,Ijustconditiononthevaluesoftheexplanatoryvariablesinthesample.Technically,thisisjustifiedbyrandomsamplingbecause,forexample,E（ui|x1,x2,…,xn）=E（ui|xi）byindependentsampling.IfindthatstudentsareabletofocusonthekeyassumptionSLR.4andsubsequentlytakemywordabouthowconditioningontheindependentvariablesinthesampleisharmless.（Ifyouprefer,theappendixtoChapter3doestheconditioningargumentcarefully.）Becausestatisticalinferenceisnomoredifficultinmultipleregressionthaninsimpleregression,IpostponeinferenceuntilChapter4.（Thisreducesredundancyandallowsyoutofocusontheinterpretivedifferencesbetweensimpleandmultipleregression.）

Youmightnoticehow,comparedwithmostothertexts,IuserelativelyfewassumptionstoderivetheunbiasednessoftheOLSslopeestimator,followedbytheformulaforitsvariance.ThisisbecauseIdonotintroduceredundantorunnecessaryassumptions.Forexample,onceSLR.4isassumed,nothingfurtherabouttherelationshipbetweenuandxisneededtoobtaintheunbiasednessofOLSunderrandomsampling.

CHAPTER3

TEACHINGNOTES

Forundergraduates,Idonotworkthroughmostofthederivationsinthischapter,atleastnotindetail.Rather,Ifocusoninterpretingtheassumptions,whichmostlyconcernthepopulation.Otherthanrandomsampling,theonlyassumptionthatinvolvesmorethanpopulationconsiderationsistheassumptionaboutnoperfectcollinearity,wherethepossibilityofperfectcollinearityinthesample（evenifitdoesnotoccurinthepopulation）shouldbetouchedon.Themoreimportantissueisperfectcollinearityinthepopulation,butthisisfairlyeasytodispensewithviaexamples.Thesecomefrommyexperienceswiththekindsofmodelspecificationissuesthatbeginnershavetroublewith.

Thecomparisonofsimpleandmultipleregressionestimates–basedontheparticularsampleathand,asopposedtotheirstatisticalproperties –usuallymakesastrongimpression.SometimesIdonotbotherwiththe“partiallingout”interpretationofmultipleregression.

Asfarasstatisticalproperties,noticehowItreattheproblemofincludinganirrelevantvariable:

noseparatederivationisneeded,astheresultfollowsformTheorem3.1.

Idoliketoderivetheomittedvariablebiasinthesimplecase.ThisisnotmuchmoredifficultthanshowingunbiasednessofOLSinthesimpleregressioncaseunderthefirstfourGauss-Markovassumptions.Itisimportanttogetthestudentsthinkingaboutthisproblemearlyon,andbeforetoomanyadditional（unnecessary）assumptionshavebeenintroduced.

Ihaveintentionallykeptthediscussionofmulticollinearitytoaminimum.Thispartlyindicatesmybias,butitalsoreflectsreality.Itis,ofcourse,veryimportantforstudentstounderstandthepotentialconsequencesofhavinghighlycorrelatedindependentvariables.Butthisisoftenbeyondourcontrol,exceptthatwecanasklessofourmultipleregressionanalysis.Iftwoormoreexplanatoryvariablesarehighlycorrelatedinthesample,weshouldnotexpecttopreciselyestimatetheirceterisparibuseffectsinthepopulation.

Ifindextensivetreatmentsofmulticollinearity,whereone“tests”orsomehow“solves”themulticollinearityproblem,tobemisleading,atbest.EventheorganizationofsometextsgivestheimpressionthatimperfectmulticollinearityissomehowaviolationoftheGauss-Markovassumptions:

theyincludemulticollinearityinachapterorpartofthebookdevotedto“violationofthebasicassumptions,”orsomethinglikethat.Ihavenoticedthatmaster’sstudentswhohavehadsomeundergraduateeconometricsareoftenconfusedonthemulticollinearityissue.Itisveryimportantthatstudentsnotconfusemulticollinearityamongtheincludedexplanatoryvariablesinaregressionmodelwiththebiascausedbyomittinganimportantvariable.

IdonotprovetheGauss-Markovtheorem.Instead,Iemphasizeitsimplications.Sometimes,andcertainlyforadvancedbeginners,IputaspecialcaseofProblem3.12onamidtermexam,whereImakeaparticularchoiceforthefunctiong（x）.Ratherthanhavethestudentsdirectlycomparethevariances,theyshouldappealtotheGauss-MarkovtheoremforthesuperiorityofOLSoveranyotherlinear,unbiasedestimator.

CHAPTER4

TEACHINGNOTES

AtthestartofthischapterisgoodtimetoremindstudentsthataspecificerrordistributionplayednoroleintheresultsofChapter3.ThatisbecauseonlythefirsttwomomentswerederivedunderthefullsetofGauss-Markovassumptions.Nevertheless,normalityisneededtoobtainexactnormalsamplingdistributions（conditionalontheexplanatoryvariables）.IemphasizethatthefullsetofCLMassumptionsareusedinthischapter,butthatinChapter5werelaxthenormalityassumptionandstillperformapproximatelyvalidinference.Onecouldarguethattheclassicallinearmodelresultscouldbeskippedentirely,andthatonlylarge-sampleanalysisisneeded.But,fromapracticalperspective,studentsstillneedtoknowwherethetdistributioncomesfrombecausevirtuallyallregressionpackagesreporttstatisticsandobtainp-valuesoffofthetdistribution.IthenfinditveryeasytocoverChapter5quickly,byjustsayingwecandropnormalityandstillusetstatisticsandtheassociatedp-valuesasbeingapproximatelyvalid.Besides,occasionallystudentswillhavetoanalyzesmallerdatasets,especiallyiftheydotheirownsmallsurveysforatermproject.

Itiscrucialtoemphasizethatwetesthypothesesaboutunknownpopulationparameters.ItellmystudentsthattheywillbepunishediftheywritesomethinglikeH0:

 =0onanexamor,evenworse,H0:

.632=0.

OneusefulfeatureofChapter4isitsillustrationofhowtorewriteapopulationmodelsothatitcontainstheparameterofinterestintestingasinglerestriction.Ifindthisiseasier,boththeoreticallyandpractically,thancomputingvariancesthatcan,insomecases,dependonnumerouscovarianceterms.Theexampleoftestingequalityofthereturntotwo-andfour-yearcollegesillustratesthebasicmethod,andshowsthattherespecifiedmodelcanhaveausefulinterpretation.Ofcourse,somestatisticalpackagesnowprovideastandarderrorforlinearcombinationsofestimateswithasimplecommand,andthatshouldbetaught,too.

OnecanuseanFtestforsinglelinearrestrictionsonmultipleparameters,butthisislesstransparentthanattestanddoesnotimmediatelyproducethestandarderrorneededforaconfidenceintervalorfortestingaone-sidedalternative.Thetrickofrewritingthepopulationmodelisusefulinseveralinstances,includingobtainingconfidenceintervalsforpredictionsinChapter6,aswellasforobtainingconfidenceintervalsformarginaleffectsinmodelswithinteractions（alsoinChapter6）.

Themajorleaguebaseballplayersalaryexampleillustratesthedifferencebetweenindividualandjointsignificancewhenexplanatoryvariables（rbisyrandhrunsyrinthiscase）arehighlycorrelated.ItendtoemphasizetheR-squaredformoftheFstatisticbecause,inpractice,itisapplicablealargepercentageofthetime,anditismuchmorereadilycomputed.Idoregretthatthisexampleisbiasedtowardstudentsincountrieswherebaseballisplayed.Still,itisoneofthebetterexamplesofmulticollinearitythatIhavecomeacross,andstudentsofallbackgroundsseemtogetthepoint.

CHAPTER5

TEACHINGNOTES

Chapter5isshort,butitisconceptuallymoredifficultthantheearlierchapters,primarilybecauseitrequiressomeknowledgeofasymptoticpropertiesofestimators.Inclass,Igiveabrief,heuristicdescriptionofconsistencyandasymptoticnormalitybeforestatingtheconsistencyandasymptoticnormalityofOLS.（Conveniently,thesameassumptionsthatworkforfinitesampleanalysisworkforasymptoticanalysis.）Moreadvancedstudentscanfollowtheproofofconsistencyoftheslopecoefficientinthebivariateregressioncase